Do hyperbolic and elliptic versions coexist with Euclidean Space-time?

These illustrations may demonstrate [not prove] how Euclidean space [anthropic perspective] may coexist with hyperbolic space of Gaussian curvature and elliptic space of Riemannian curvature. [The hyperbola is reciprocal to the ellipse in eccentricity - the R:1/R relationship?] Is it possible that one can alternately be nested within the other as planets in a solar system within a local bubble within a galaxy within a cluster?

2 - Why the helix may be the geodesic of all mechanical [and electrical?] motion -
This Japanese website [author: iittoo?] in English has numerous elliptic and hyperbolic examples.
http://www1.kcn.ne.jp/~iittoo/index.html#chapters [Broken]

The most interesting may be the tractoid or pseudosphere - perhaps related to the structure of rotating spiral galaxies.
Figures 6, 6’ illustrate how the helix may be a geodesic for the moving tractoid.
Figure 16 is credited to Tore Nordstrand from Gallery of Curved Surfaces [French].
This may illustrate how a solar system or galaxy may retain the logarithmic spiral as they move through space-time.
http://www1.kcn.ne.jp/~iittoo/us20_pseu.htm [Broken]